"To cite" is a verb that is a synonym for "to quote".

From the verb "to cite" we derive the adjective "cited".

"Cited" means that something has been quoted by somebody. Somebody has referred to it.

"Well-cited" would mean that it has been quoted many times by many different people.

When I first read the question, my first thought was that well-cited means the source citation is done well.  In other words, every piece of information has its source cited and the citation is done in the proper format.  

Then I read Elizabeth's response and now I'm more inclined towards her answer. 

It depends :-)

I am guessing the request is coming from a teacher -- they either want you to use well-cited articles or to create one yourself.

If you are to use well-cited articles in your research you are looking either for articles/books that have been often quoted by other researchers in the field.  You can then be assured the research is well respected.

Or perhaps you have an article that makes many interesting points, and in each point the author quotes definitive sources for his facts, usually as footnotes in the article.  That means his article has a lot of source material backing up his conclusions, it is a well-cited article.

Or perhaps your teacher is looking for you to write a well cited article.  In that case the teacher wants you to do research, write your observations and conclusions, and clearly attribute facts and the conclusions of other authors to their sources.  An article on how to do that is here:

https://www.quora.com/How-can-I-write-a-well-cited-article-in-my-field

https://www.e-education.psu.edu/styleforstudents/c5_p8.html

heh, I just wrote a well-cited article :-)

neal